Algorithm 1. Pseudo-code of ASO algorithm.

1: Input: upper and lower bounds of variables (xmax and xmin), dimension of the problem (D), maximum number of iterations (T), number of population (N), β, and α.

2: Initialize the velocity and position of atoms randomly.

3: Calculate the fitness of atoms.

4: Record the best solution.

5: Initialize iteration count: $t=1$.

6: while $(t\le T)$ do

7:   for i = 1 to N do

8:     Compute mass by Eqs. (13) and (14).

9:     Define subset K atoms by Eq. (2).

10:     Calculate the interaction force by Eq. (1).

11:     Compute the constraint force by Eq. (9).

12:     Calculate the acceleration by Eq. (12).

13:     Update the velocity of the atoms by Eq. (15).

14:     Update the position of atoms by Eq. (16).

15:     Check if the new position is within boundaries.

16:     Evaluate the current fitness.

17:   end for

18:    $t=t+1$.

19: end while

20: Output: Return the best solution.